I have been in your position.
The first thing to do is to remove the firing pins and clean out the whole mechanism.
If the nature of the pins means that they still tend to "stick" a bit while protruding, I have taken apart a ball point pen to add enough spring to just tend to keep the pins back.
My Blanch has pins similar to what you describe. I think their shape causes a kind of wedging action against their channels. While the rebounding hammers are kept well back of any contact, the tendency to protrude bothered me. A mere single curl of spring took care of the worry.
A few of the gunsmiths I would recommend have been in favor of this approach regardless of the age of the gun.
